Impact of axisymmetric deformation on MR elastography of a nonlinear tissue-mimicking material and implications in peri-tumour stiffness quantification

Abstract

Solid tumour growth is often associated with the accumulation of mechanical stresses acting on the surrounding host tissue. Due to tissue nonlinearity, the shear modulus of the peri-tumoural region inherits a signature from the tumour expansion which depends on multiple factors, including the soft tissue constitutive behaviour and its stress/strain state. Shear waves used in MR-elastography (MRE) sense the apparent change in shear modulus along their propagation direction, thereby probing the anisotropic stiffness field around the tumour. We developed an analytical framework for a heterogeneous shear modulus distribution using a thick-shelled sphere approximation of the tumour and soft tissue ensemble. A hyperelastic material (plastisol) was identified to validate the proposed theory in a phantom setting. A balloon-catheter connected to a pressure sensor was used to replicate the stress generated from tumour pressure and growth while MRE data were acquired. The shear modulus anisotropy retrieved from the reconstructed elastography data confirmed the analytically predicted patterns at various levels of inflation. An alternative measure, combining the generated deformation and the local wave direction and independent of the reconstruction strategy, was also proposed to correlate the analytical findings with the stretch probed by the waves. Overall, this work demonstrates that MRE in combination with non-linear mechanics, is able to identify the apparent shear modulus variation arising from the strain generated by a growth within tissue, such as an idealised model of tumour. Investigation in real tissue represents the next step to further investigate the implications of endogenous forces in tissue characterisation through MRE.

MR Elastography in Cancer

“…Magnetic resonance elastography quantification of solid stress has been demonstrated in controlled compression tests in animals; however, such tests are less well applicable in patients 40,41 . Sensitization of MRE to solid stress and tumor compression requires repeat MRE at different levels of prestress or assessment of tissue deformation induced by the growing mass 102,103 . Tissue deformation resulting from a displacing tumor mass can be derived from 3D MRI data based on the assumed undeformed geometry of the host tissue 104,105 .…”

“…40,41 Sensitization of MRE to solid stress and tumor compression requires repeat MRE at different levels of prestress or assessment of tissue deformation induced by the growing mass. 102,103 Tissue deformation resulting from a displacing tumor mass can be derived from 3D MRI data based on the assumed undeformed geometry of the host tissue. 104,105 Multiplying 3D deformation grids with MRE-derived in vivo stiffness could provide maps of local solid stresses in a tumor and its surrounding tissue.…”